Extra-Trees splitting algorithm (for numerical attributes)

Split a node(S)
Input: the local learning subset S corresponding to the node we want to split
Output: a split [a < ac] or nothing
– If Stop split(S) is TRUE then return nothing.
– Otherwise select K attributes {a1, . . . , aK } among all non constant (in S) candidate attributes; –DrawKsplits{s1,…,sK},wheresi =Pick a random split(S,ai),∀i =1,…,K;
– Return a split s∗ such that Score(s∗, S) = maxi=1,…,K Score(si , S).

Pick a random split(S,a)
Inputs: a subset S and an attribute a
Output: a split
– Let amS ax and amS in denote the maximal and minimal value of a in S; – Draw a random cut-point ac uniformly in [amS in , amS ax ];
– Return the split [a < ac].

Stop split(S)
Input: a subset S
Output: a boolean
– If |S| < nmin, then return TRUE;
– If all attributes are constant in S, then return TRUE; – If the output is constant in S, then return TRUE;
– Otherwise, return FALSE.

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